Irreducible mod $p$ Lubin-Tate $(\varphi,\Gamma)$-modules

TL;DR

This paper classifies the Lubin-Tate $(, abla)$-modules linked to absolutely irreducible mod $p$ Galois representations over finite extensions of $Q_p$, advancing understanding of their structure.

Contribution

It explicitly determines the Lubin-Tate $(, abla)$-modules for all absolutely irreducible mod $p$ Galois representations over finite extensions of $Q_p$, a novel classification result.

Findings

Complete description of associated Lubin-Tate $(, abla)$-modules.

Identification of the structure of irreducible mod $p$ Galois representations.

Extension of known classifications to more general local fields.

Abstract

Let $F$ be a finite extension of $\mathbb{Q}_p$. We determine the Lubin-Tate $(\varphi,\Gamma)$-modules associated to the absolutely irreducible mod $p$ representations of the absolute Galois group ${\rm Gal}(\bar{F}/F)$.